Question

It is possible to write a simple Lewis structure for the \(\mathrm{SO}_{4}^{2-}\) ion, involving only single bonds, which follows the octet rule. However, Linus Pauling and others have suggested an alternative structure, involving double bonds, in which the sulfur atom is surrounded by six electron pairs. (a) Draw the two Lewis structures. (b) What geometries are predicted for the two structures? (c) What is the hybridization of sulfur in each case? (d) What are the formal charges of the atoms in the two structures?

Short answer

Based on the analysis of Lewis structures, geometries, hybridizations, and formal charges, the most accurate representation of the \(\mathrm{SO}_{4}^{2-}\) ion is the structure with one double bond between Sulfur and an Oxygen atom, proposed by Linus Pauling. The geometry is octahedral, and the hybridization of Sulfur is sp³d² in this structure.

Step-by-step solution

(a) Drawing the two Lewis structures

First, we will draw the Lewis structures for the two cases - single and double bonds: 1. For the single bond case, we can start by placing Sulfur in the center and connect it with single bonds to each of the four Oxygen atoms. Then, complete the octet of each Oxygen atom by adding six more electrons according to the octet rule. 2. For the double bond case, one of the double bonds is placed between Sulfur and an Oxygen atom, while the other three Oxygen atoms are attached with single bonds. Complete the octet of each Oxygen atom by adding the required number of electrons (four more for the double-bonded Oxygen, and six more for single-bonded Oxygen atoms).

(b) Predicting geometries

For the geometries of the two structures, we will use the VSEPR (Valence Shell Electron Pair Repulsion) theory, which states that the arrangement of electron pairs around the central atom is determined by minimizing repulsion between the electron pairs. 1. In the single bond case, Sulfur has four electron pairs - one bonded to each Oxygen atom and no lone pairs. According to VSEPR theory, the geometry of this structure would be tetrahedral. 2. In the double bond case, Sulfur has six electron pairs - one double bond with an Oxygen atom, three single bonds with other Oxygen atoms, and no lone pairs. With six pairs, the geometry of this structure would be octahedral.

(c) Hybridization of sulfur

To determine the hybridization of sulfur in each case, we will look at the number of electron domains surrounding it: 1. In the single bond case, Sulfur has four electron domains - each consisting of one single bond with an Oxygen atom. The hybridization required for four electron domains is sp³. 2. In the double bond case, Sulfur has six electron domains - one double bond and three single bonds. The hybridization required for six electron domains is sp³d².

(d) Calculating formal charges

To calculate the formal charges of atoms in both structures, we will use the formula: Formal charge = (Valence electrons) - (Lone pair electrons) - (1/2 × Bonding electrons) 1. In the single bond case: - Sulfur: Formal charge = (6) - (0) - (1/2 × 8) = 0 - Oxygen (each): Formal charge = (6) - (6) - (1/2 × 2) = -1 Since there are four oxygen atoms with -1 formal charge, the net charge on the ion is -2. 2. In the double bond case: - Sulfur: Formal charge = (6) - (0) - (1/2 × 12) = +1 - Double-bonded Oxygen: Formal charge = (6) - (4) - (1/2 × 4) = 0 - Single-bonded Oxygen (each): Formal charge = (6) - (6) - (1/2 × 2) = -1 Net charge on the ion is (+1) + 3 × (-1) = -2. Considering the formal charges in both structures, the structure with the double bond more closely matches the -2 charge on the sulfate ion, suggesting that the Linus Pauling's alternative structure with double bonds is a better representation of the \(\mathrm{SO}_{4}^{2-}\) ion.

Key concepts

VSEPR Theory

The VSEPR theory, or Valence Shell Electron Pair Repulsion theory, is a model in chemistry used to predict the geometry of individual molecules based on the idea that electron pairs around a central atom will repulse each other. This repulsion is due to the negative charge that electrons carry, and hence they will try to stay as far apart as possible.

According to VSEPR theory, the most stable arrangement minimizes the repulsion among all the electron pairs. This arrangement is influenced by the total number of bonding and non-bonding electron pairs (also known as electron domains) in the valence shell of the central atom. For example, if a molecule has four electron domains, VSEPR theory predicts a tetrahedral geometry. If there are six electron domains, the geometry would be octahedral.

When finding geometries for Lewis structures, it's crucial to consider VSEPR theory to accurately represent molecular shapes. This theory helps to explain why certain molecules have specific shapes and angles between bonds, which are critical properties affecting the molecule's function and reactivity in various chemical environments.

Hybridization

Hybridization is a concept in molecular chemistry that describes the bonding situation within a molecule. It is the process by which atomic orbitals combine to form new hybrid orbitals that are suitable for the pairing of electrons to form chemical bonds. This process allows atoms to achieve a more stable electron configuration.

The type of hybridization depends on the number of electron domains around the central atom. For instance:

• If there are four electron domains, the central atom is said to undergo sp³ hybridization, which reflects the formation of four sp³ hybrid orbitals.
• If there are six electron domains, the hybridization becomes sp³d², indicating the formation of six hybrid orbitals.

Knowing the hybridization of an atom is crucial as it determines the molecule's geometry and how it will interact with other molecules. It also helps in understanding the distribution of electrons around the atom and the types of bonds it can form.

Formal Charge Calculation

Calculating the formal charge of an atom within a molecule is a critical step in validating the stability and viability of a proposed Lewis structure. The formal charge is a bookkeeping tool that compares the number of valence electrons in an isolated atom with the number of valence electrons assigned to that atom in a molecule.

To calculate the formal charge, the formula used is:\[\begin{equation}Formal\ charge = (\text{Valence electrons}) - (\text{Lone pair electrons}) - (\frac{1}{2} \times \text{Bonding electrons})\end{equation}\]
For example, if an oxygen atom has six valence electrons, two lone pairs, and forms a single bond (which accounts for two bonding electrons), its formal charge would be:\[\begin{equation}Formal\ charge = 6 - (2 \times 2) - (\frac{1}{2} \times 2) = 0\end{equation}\]
Understanding formal charge helps determine the most appropriate Lewis structure for a molecule because the structure with formal charges closest to zero is often the most stable. This approach provides insight into the charge distribution within a molecule, predicting reactivity and interaction with other molecules.